Determination of Protein-Ligand Binding Constants Using a Spectroscopy

Protein-ligand interactions are studied across many scientific disciplines. Understanding these interactions allows one to further understand how many systems within the human body works. When a protein binds to a ligand, a change occurs that alters a reaction and results in a cascade. An example would be the interactions involved in the uptake of 02 by hemoglobin, where binding inaugurates the transport of molecular oxygen throughout the vascular system (2).

Optimal conditions are considered when studying protein-ligand interactions because different conditions are known to be more ideal than others for the reaction. To determine what the optimal condition is, protein-ligand constants are calculated and compared. Using spectrophotometric methods, a protein-ligand binding constant was calculated under five pH environments within five studies in order to evaluate the ideal pH conditions for this protein to find to the ligand. For this report, BSA acts as the protein and MO acts as the ligand.

There are multiple binding sites for a ligand within a protein molecule (3). The affinity of a binding site for a specific ligand depends on whether or not the other sites are occupied (3). To appropriately evaluate the differences in these protein-ligand equilibria constants for each protein, the concept of multiple bind sites must be accounted for.

We can first take the formula for equilibria where P and L stand for the ligand (L) and free protein (P):
P + L ? PL

(1)
K is the binding constant that can be defined as:
K =
PL

(2)
P x L
The following equation us used to accommodate for the proteins and ligands that do not bind to each other (for in this case, the concentration of protein is much larger than that of ligand, i.e. [P] >>> [L]):

Pt = P + PL or P = Pt - PL

(3)
Lt = L + PL or L = Lt - PL

(4)
These two equations can be substituted into the original equation for K so that:

K =

PL

(5)
(Pt - PL)( Lt - PL)

In evaluation of Beer's Law (which will be used because the method in this report is spectrophotometric and therefore requires Beer's Law. Absorbance is defined as:
A = ?bc